While we are a democratic republic in theory, we more truly resemble an oligarchy.

The power in the United States in the hands of the wealthy elite. Money can be donated by corporations to political campaigns in massive amounts with little to no regulation at all. The cost of this support is all too often a promise to represent the interests of the corporation on Capitol Hill. Additionally, the Electoral College makes it so that the votes of the People don't necessarily decide the outcome of a Presidential election.

Not just corruption, there are flaws in the system itself.

The "weight" of your vote depends on which state you're voting in. States (according to size of population) get electorial votes that are the real votes which are used rather than the individual ones. The thing is that the side who wins- no matter how small the majority- gains all votes the state has, even if it's 51% over 49%. Elections can also be rigged by gerrymandering.

Another thing is that this "according to size" thing isn't very accurate. Samll states get more votes than they should and those extra votes for small ones come from bigger ones. Just imagine this nonsense , one small state vote (of a citizen, not electorial) is worth 3 - 4 texan votes. Because small states get more electorial votes than they should you can win presidential elections just by gaining 25% of peoples votes in small states.

(I thing you should watch a video about it from C.G.P. Grey on youtube , he explains things better than me)

They never appeared that democratic,

And in 2010 the gang of 5 made it official. Under the terms of citizens united, bribery and backmail are now the law of the land. No matter who wins the vote, the politicians will answer to their ruling-class campaign sponsors and not the voters. The lousy economy since then is no accident either.